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What acceleration gives a velocity vs. time plot that is (a) a
straight line with a slope of +0.5 m/s each second? (b) a straight
line with a slope of -0.5 m/s each second? (c) a straight line with
a slope of +0.5 m/s each second until t = 5 s, and thereafter as
horizontal line?

Conceptualize
The particle moves with an acceleration that can switch abruptly
between being positive or negative, corresponding to velocity
changes that follow being in either the positive or negative
direction.

Categorize
The question is about motion in one dimension, and the relation
between velocity and acceleration when the acceleration is constant
except for abrupt changes in sign.

(A) Acceleration for a straight line velocity-time plot with upward
slope. Analyze For a straight line velocity vs. time plot with an
upward slope of +0.5 m/s2, the velocity increases by the same
amount for each second of time that passes. The velocity changes by
_______m/s for each second that passes. This is a constant
(positive/negative) **POSITIVE OR NEGATIVE?** acceleration.

(B) Acceleration for a straight line velocity-time plot with
downward slope. Analyze For the straight line velocity vs. time
plot that has a downward slope of -0.5 m/s2, the velocity changes
by _______m/s for each second that passes. This is a constant
(positive/negative) **POSITIVE OR NEGATIVE?** acceleration.

(C) Acceleration with a slope of +0.5 m/s each second until t = 5
s, and thereafter constant. Analyze In this case the velocity gains
+0.5 m/s for each second that passes until the total velocity
increase is _____m/s. Thereafter, the velocity is constant, so that
the acceleration is ____m/s2.